what would be the differentiation of 2^3^x^2?

Question

so that is 2 to the 3 to the x to the 2... each is an exponent of one other...

the answer i got is 2^3^x^2 * ln 2 * 3^x^2 * x^2 * 2x

is that right? my friend had the same, except she did not have x^2 in it.

please correct!!

Answer 1

let y = 2^(3^(x^2))

ln y = x^2 ln(2^3)
ln y = ln8(x^2)

(dy/dx)/y = (2ln8)x

dy/dx = (2ln8)xy
=(2ln8)x(2^(3^(x^2)))